[2602.03773] Reasoning Cache: Continual Improvement Over Long Horizons via Short-Horizon RL

Computer Science > Machine Learning arXiv:2602.03773 (cs) [Submitted on 3 Feb 2026 (v1), last revised 22 Mar 2026 (this version, v2)] Title:Reasoning Cache: Continual Improvement Over Long Horizons via Short-Horizon RL Authors:Ian Wu, Yuxiao Qu, Amrith Setlur, Aviral Kumar View a PDF of the paper titled Reasoning Cache: Continual Improvement Over Long Horizons via Short-Horizon RL, by Ian Wu and 3 other authors View PDF Abstract:Large Language Models (LLMs) that can continually improve beyond their training budgets are able to solve increasingly difficult problems by adapting at test time, a property we refer to as extrapolation. However, standard reinforcement learning (RL) operates over fixed problem distributions and training budgets, which limits extrapolation amidst distribution shift at test time. To address this, we introduce RC, an iterative decoding algorithm that replaces standard autoregressive decoding during both training and inference. RC exploits an asymmetry between the response generation and summarization capabilities of LLMs to construct reasoning chains that consistently improve across iterations. Models trained to use RC can extrapolate and continually improve over reasoning horizons more than an order of magnitude longer than those seen during training. Empirically, training a 4B model with RC using a 16k-token training budget improves performance on HMMT 2025 from 40% to nearly 70% with 0.5m tokens at test time, outperforming both comparably sized mo...